Solve for $x$ and $y$ using elimination. ${-4x+4y = -12}$ ${5x+3y = 39}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-3$ and the bottom equation by $4$ ${12x-12y = 36}$ $20x+12y = 156$ Add the top and bottom equations together. $32x = 192$ $\dfrac{32x}{{32}} = \dfrac{192}{{32}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-4x+4y = -12}\thinspace$ to find $y$ ${-4}{(6)}{ + 4y = -12}$ $-24+4y = -12$ $-24{+24} + 4y = -12{+24}$ $4y = 12$ $\dfrac{4y}{{4}} = \dfrac{12}{{4}}$ ${y = 3}$ You can also plug ${x = 6}$ into $\thinspace {5x+3y = 39}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ + 3y = 39}$ ${y = 3}$